# Measurement of acceleration using light gates

##### Demonstration

This activity uses light beams and timing technology to obtain values for acceleration.

#### Apparatus and materials

Scaler or datalogging timing system

Light beam assemblies (sources and sensors), 2

Dynamics trolley

Runway, with means to produce a uniform slope

Elastic cords with means of fixing them to the trolley, 3

Card

Stopwatch or stopclock

#### Health & Safety and Technical notes

A long runway is too heavy for one person to carry and manipulate: ensure that two persons are available to set it up.

Whichever device you use, you will need to know how it operates.

The card should be 10 or 20 cm long and 5 or 6 cm wide.

Depending on the timing device, the lamps and sensors may be connected separately to the timer, or both of them connected in series with the timer. #### Procedure a Put the trolley on the runway and adjust the slope so that, when you give the trolley a push, it rolls at a near-steady speed. The force of gravity now compensates for the effects of friction. The trolley behaves approximately as if there were no friction.

b Set up the two light beam source and sensor pairs, at least one metre apart, along the runway near to the beginning and end of the trolley's journey.

c Fix the card to the trolley so that it breaks the light beam between both source and sensor pairs as it moves down the runway.

d Pull the trolley along the runway, starting from above the first light beam, with a constant force. Use a single elastic cord to do this, keeping it at a fixed amount of stretch or extension. (Aligning the end of the cord with the front edge of the trolley enables you to keep it at constant length.)

e Measure the times for which the card is blocking each of the light beams. If you are using a scaler then you will need to read the first time before the trolley gets to the second beam. If you are using a datalogging system then it will record both of the times.

f The distance travelled by the trolley during the two measured times is the width of the card. Divide distance by time in each case to work out the two velocities.

g To work out acceleration, you need to know the time that the trolley takes to travel from one beam to the other. If you are using a scaler system, you will need to use a separate stopwatch or stopclock for this. Your datalogging system may be capable of measuring the time directly.

h Use a = (v - u)/t to find the trolley's acceleration, where a = acceleration, v = final velocity, u = initial velocity, t = time between u and v

#### Teaching notes

1 This measurement of acceleration takes little time once you have set up the apparatus. Let the students take their own measurements in groups of two or more.

2 You can extend the activity beyond the simple measurement of acceleration to an investigation of the dependence of acceleration on applied force or on mass. Force can be varied simply by adding more elastic cords in parallel. Each extra cord, all of them always stretched by the same amount, adds an extra 'unit' of force. You can vary mass by stacking trolleys one above the other, using the metal rods supplied.

3 The activity raises issues of the distinction between average and instantaneous values of velocity and acceleration. If the cards were of vanishing width, they would give values of distance and time for a single instant. This is of course impossible, but the resulting calculated velocity would be the velocity at that single instant. (Note that a speedometer does supply values of practically instantaneous velocities, so it is not merely a theoretical concept.) Since the card has a finite width, the recorded values of distance and time give the velocities averaged over the fairly short times for which the card breaks the beams.

4 Even with instantaneous values of velocities, this experiment yields information about average acceleration during the time between the two measurements. It does not measure the acceleration instant by instant as the trolley travels. However, since force and mass are constant, acceleration is constant. Thus the average acceleration and its acceleration at any instant are, in fact, the same.

5 If the timing device does not appear to count correctly:

• try adjusting the relative position of the lamp and detector to get maximum illumination of the latter
• try reversing the polarities of the detector.

This experiment was safety-checked in December 2004